Introduction to algorithms: orders the N numbers between [0 .. n ^-1] In 8.3-4 O (n) time.

I. Question

How to sort the N integers between 0 and N ^ 2-1 in O (n) Time

 

Ii. Train of Thought to convert the integer into N in hexadecimal order and then sort the number. Each number has two digits. The value range of each digit is [0 .. n-1], and then sort the base number.

 

Iii. Code [CPP]
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1. # Include <iostream>
2. # Include <cmath>
3. Using namespace STD;
5. Int N, Radix, length_a, digit = 2;
6. Void print (int * a, int start, int end)
7. {
8. Int I;
9. For (I = start; I <= end; I ++)
10. {
11. If (I = Start) cout <'{';
12. Else cout <'';
13. Cout <A [I];
14. }
15. Cout <'}' <Endl;
16. }
17. // Stable sorting of base sort calls
18. Void stable_sort (int * a, int * B, int K, int D)
19. {
20. Int I, J;
21. // Initialize the C array to 0 for counting
22. Int * c = new int [k + 1];
23. For (I = 0; I <= K; I ++)
24. C [I] = 0;
25. Int * D = new int [length_a + 1];
26. For (j = 1; j <= length_a; j ++)
27. {
28. // D [J] indicates the I-digit number of the [J] Element
29. D [J] = A [J] % (INT) Pow (Radix * 1.0, d)/(INT) Pow (Radix * 1.0, D-1 );
30. // C [J] indicates the number of times the number d [J] appears in array.
31. C [d [J] ++;
32. }
33. // C [I] indicates the number of times that the <= I number has appeared.
    
34. For (I = 1; I <= K; I ++)
35. C [I] = C [I] + C [I-1];
36. // Initialize B to 0 and B to output the sorting result
37. For (I = 1; I <= length_a; I ++)
38. B [I] = 0;
39. For (j = length_a; j> = 1; j --)
40. {
41. // If the number of numbers <= d [J] is X, after sorting, a [J] should appear at position X, that is, B [x] = A [J]
    
42. B [C [d [J] = A [J];
43. C [d [J] --;
44. }
45. Delete [] C;
46. Delete [] D;
47. }
48. // Base sorting
49. Void radix_sort (int * a, int * B)
50. {
51. Int I, J;
52. // Sort each bit in sequence, from low to high
53. For (I = 1; I <= digit; I ++)
54. {
55. Stable_sort (a, B, Radix-1, I );
56. // The input is A, the output is B, and the output data should be put into the output data when sorting again
    
57. For (j = 1; j <= length_a; j ++)
58. A [J] = B [J];
59. }
60. }
62. Int main ()
63. {
64. Cin> N;
65. Length_a = N;
66. Int * A = new int [n + 1];
67. Int * B = new int [n + 1];
68. Bool flag [1000] = {0 };
69. Int I;
70. // Generate n random data ranges from 0 to N ^-1.
71. For (I = 1; I <= N; I ++)
72. {
73. Do
74. {
75. A [I] = rand () % (n * n );
76. } While (flag [A [I]);
77. Flag [A [I] = 1;
78. }
79. Print (A, 1, n );
80. Radix = N;
81. Radix_sort (A, B );
82. Print (A, 1, n );
83. Return 0;
84. }

Reprinted from: http://blog.csdn.net/mishifangxiangdefeng/article/details/7685839